Page:Philosophical Transactions of the Royal Society A - Volume 184.djvu/847

presence of dense matter (water-filled telescopes) or otherwise (cf. ‘Nature,’ vol. 46, p. 498).

However matter affects or loads the ether inside it, it cannot on this theory be said to hold it still, or carry it with it. The general ether stream must remain unaffected, not only near, but inside matter, if rays are to retain precisely the same course as if it were relatively stationary.

But it must be understood that the ethereal motion here contemplated is the general drift of the entire medium, or its correlative the uniform motion of all the matter con cerned. There is nothing to be said against aberration effect being producible or modi fiable by motion of parts of the medium, as, for instance, by sliding one portion of the ether past another portion, as by the artificial motion of slabs and other partitioned-off regions. These matters are to some extent mixed up with the law of refraction, which we consider later, but the general ideas concerning them have been already given. Artificial motion of matter may readily alter both the time of journey and the path of a ray (cf. §§ 7 and 52).

Effect of placing Ordinary Matter in the path of a ray in a Drifting Medium.
Fresnel's Law a special case of a universal Potential-function.

28. Inside a transparent body light travels at a speed $\mathrm {V} /\mu$; and the ether, which outside drifts at velocity $v$ making an angle $\theta$ with the ray, inside may be drifting with velocity $v^{\prime }$ and angle $\theta ^{\prime }$. Hence the equation to a ray inside such matter is

$\mathrm {T} ^{\prime }=\int {\frac {ds}{\left(\mathrm {V} /\mu \right)\cos \epsilon ^{\prime }+v^{\prime }\cos \theta ^{\prime }}}=$ min., where ${\frac {\sin \epsilon ^{\prime }}{\sin \theta ^{\prime }}}={\frac {v^{\prime }}{\mathrm {V} /\mu }}=\alpha ^{\prime }$.

This may be written

$\mathrm {T} ^{\prime }=\int {\frac {\cos \epsilon ^{\prime }ds}{\mathrm {V} /\mu \left(1-\alpha ^{\prime 2}\right)}}-\int {\frac {v^{\prime }\cos \theta ^{\prime }ds}{\mathrm {V} ^{2}/\mu ^{2}\left(1-\alpha ^{\prime 2}\right)}}$;

the second term alone involves the first power of the motion, and assuming that $\mu ^{2}v^{\prime }\cos \theta ^{\prime }=d\phi ^{\prime }/ds$, and treating $\alpha ^{\prime 2}$ as a quantity too small for its possible variations to need attention, the expression becomes

$\mathrm {T} ^{\prime }=\mu \mathrm {T} {\begin{matrix}\cos \epsilon ^{\prime }\\1-\alpha ^{\prime 2}\end{matrix}}-{\frac {\phi _{\mathrm {B} }^{\prime }-\phi _{\mathrm {A} }^{\prime }}{\mathrm {V} ^{2}\left(1-\alpha ^{\prime 2}\right)}}$,

$\mathrm {T}$ being the time of travel through the same space when empty. Now, if the time of journey and course of ray, however they be affected by the dense body, are not to be more affected by reason of ethereal drift through it than if it were so much empty